Hi. I'm trying to understand the pronunciation of the word "shén​me". There are recordings all over the Internet of native Mandarin speakers saying it: for example, here: http://www.forvo.com/word/%E4%BB%80%E4%B9%88/#zh. What's confusing me is I don't hear the second tone on "shen" when they pronounce it. It sounds almost level tone, or even down in tone. Then the tone goes way up on "me", which is supposed to be neutral. So, can anyone explain the difference here between what I expected and what I hear? Is there some exception to the usual rules?

I'm pretty sure what you're hearing isn't an exception, but just people being more free with their speaking. It can often be difficult to pick the second and third tones apart from each other, so that might be what you're experiencing. Also, there will be many times where people don't speak clearly and you'll hear something a touch different that you learned. After all, not everyone speaks perfectly standard Mandarin even if they're Chinese.

In my experience the neutral tone is just kind of a "do whatever you want" sort of thing. For that reason it also seems to carry a bit of a tone, but it varies on the mood of the person or the cadence of the sentence.